Recent content by paraboloid

1. Derive Wirtinger derivatives

Let \bar{z} = x+iy. We are given that x = \frac{z+\bar{z}}{2} & y = \frac{z-\bar{z}}{2i}. We are trying to derive \partial F/\partial\bar{z} = 1/2(\partial F/ \partial x + i \partial F/ \partial y), where F(x,y) is some function of two real variables. Using the chain rule I get \partial...
2. Initial Value Problem with Laplace Transforms

Solve the following given y(0) = 0 & y'(0)=1: y′′+3y′+2y = u2(t), such that u2(t) is a heaviside step function Here's what I've got so far, =>s2Y(s)−sy(0)−y′(0) + 3sY(s)−3y(0) + 2Y(s)= exp(−2s)/s Y(s) = (exp(−2s) + s) / (s(s2+3s+2)) Y(s) = exp(−2s)/(s(s2+3s+2))* + 1/(s2+3s+2)** The...
3. Determine the indicated roots of the complex number

Thanks everyone for your input. Much appreciated.
4. Determine the indicated roots of the complex number

The answer in the back is actually +/-(sqrt 3 + i) / sqrt(2). The text doesn't specify how many roots to find, but it looks like two roots. I believe i've converted it to the latter form(k = 0), but I'm still unsure what more I need to do to get the roots.
5. Determine the indicated roots of the complex number

[2(cos(pi/3)+isin(pi/3))]1/2 I simplified it to 21/2(cos(pi/6)+isin(pi/6)), but I have no idea what else to go to. Any tips would be very helpful, thx in advance
6. Linear Differential Problem(Pollutants into a lake)

Hi, This is my problem: Consider a lake of constant volume V containing at time t an amount Q(t) of pollutant, evenly distributed throughout the lake with a concentration c(t), where c(t) = Q(t)/V . Assume that water containing a concentration k of pollutant enters the lake at a rate r...
7. Changing the order of a triple integration

I'm given this definite integral: \int_0^{1}\int_{\sqrt{x}}^{1}\int_{0}^{1-y}f(x,y,z)dzdydx I need to change the order to dydxdz, but I'm stuck trying to get the limits of integration wrt y. \int_0^{1}\int_{x^2}^{0}\int_{}^{}f(x,y,z)dydzdx How do I find the limits of y?
8. Find the center of mass of a lamina

That is a very good strategy I overlooked. Thanks so much.
9. Find the center of mass of a lamina

The boundary of a lamina consists of the semicircles y=\sqrt{1-x^2} and y=\sqrt{4-x^2} together with the portions of the x-axis that join them. Find the center of mass of the lamina if the density at any point is proportional to its distance from the origin. I drew a graph that looks like...
10. Using polar coordinates to find the volume of a bounded solid

I think that's the root of my problem. I found a http://answers.yahoo.com/question/index?qid=20080327174835AA36kOs" that's similar, but it doesn't show the work to get the integrand.
11. Using polar coordinates to find the volume of a bounded solid

Using polar coordinates to find the volume of a bounded solid[Solved] I found the equation of the boundary circle by setting z to 4 in the paraboloid. Then I did some work to get polar coords: x^2+y^2 = 1 x^2+y^2 = r^2 1-x^2-y^2 = 1-r^2 Then I set up my integral as such...
12. Volume of Tetrahedron

Thank you both! I'll definitely work on my latex once things settle down so that I don't cause so much confusion. And yes, in fact I add 24 to -168 instead of subtracting.
13. Volume of Tetrahedron

Volume of Tetrahedron[Solved] My text book opts to integrate with respect to y before x(dydx vs dxdy), so I assumed that it would not affect the outcome. I set the upper and lower bounds of y, respectively, as y = 24 - 7x/4 (from 7x+4y=96) to y = x/4 (from x = 4y). For x I set it from...
14. How fast is the distance between the cars changing at this moment

Good call. Thanks Dick!
15. How fast is the distance between the cars changing at this moment

[Solved]How fast is the distance between the cars changing at this moment I'm in need of help with the last part (finding dz/dt). I'm sorry I don't know how to use latex. Let D refer to partial derivatives. This was my attempt best try: Given dz/dt = Dz/Dt*dx/d+ Dz/Dt*dy/dt and z...